In 1989, a generalized approach based on signal flow graph methods for designing filters with only transconductance elements and grounded capacitors was presented [1]. For generating active simulations of the LC-ladder filters, the methods result in circuits where all transconductors except one are identical, making the approach extremely convenient for monolithic realization with systematic design and dense layout Although derived for single-input transconductance elements, it is shown how the methods can be extended to designs based on differential: input or even fully balanced transconductors. As an example, the method employs 23 single-input OTAs and 10 grounded capacitors to realize an eighth-order elliptic band-pass LC-ladder filter. In 1991, a third-order elliptic low-pass filter was proposed [2] which employed 3 single-input OTAs, 5 double-input OTAs and 4 grounded capacitors. In 1993, an OTA-C realization of general voltage-mode nth-order transfer functions, which is different from simulating passive ladders [1], was presented [3] which used n double-input OTAs, n+2 single-input OTAs and n grounded capacitors. In 1994, a technique employing 3 single-ended-input OTAs, 4 double-input OTAs, and 4 grounded capacitors to realize third-order elliptic filters was presented [4]. In 1994, a methodology to compensate for the non-ideal performance of the OTA, a current-mode filter using single-input multiple-output OTAs and based on RLC ladder filter prototypes was presented [5]. It realized a 5th-order all-pole RLC ladder filer by using seven single-input OTAs, and 5 grounded capacitors, and a third-order elliptic low-pass filter by using seven single-input OTAs, three grounded capacitors and 2 current buffers.
Employing a current-mode integrator and a proportional block as basic building units to reduce the component count, a current-mode nth-order filter configuration was introduced in 1996 [6]. It employs n+2 single-input OTAs and n grounded capacitors. In the same year, the voltage-mode filter structure proposed in [7] employs n+1 single-input OTAs, n−1 double-input OTAs, and n grounded capacitors in order to realize an nth-order voltage-mode transfer function but without the nth-order term in the numerator. On the other hand, employing 2n+2/2n+3 single-input OTAs and n grounded capacitors to realize an nth-order current-mode general transfer function was also proposed [14]. A systematic generation of current-mode dual-output OTA filters using a building block approach was developed in 1997 [8]. It uses four single-input OTAs and two grounded capacitors to realize a second-order high-pass or notch, namely, band-reject filter under some component matching conditions. In the same year, employing n double-input OTAs, n+2 single-input OTAs, and n grounded capacitors to realize a general nth-order voltage-mode transfer function was proposed [9]. In 1998, a design approach based on simulating RLC ladder networks using coupled-biquad structures was presented [10]. Applying this approach, it needs 7 single-input OTAs, and 7 grounded capacitors to realize a fifth-order all-pole low-pass ladder filter, needs 9 single-input OTAs, and 6 grounded capacitors to realize a sixth-order all-pole band-pass ladder filter, and needs five OTAs, one of which is double-input OTA, four grounded capacitors, and a current buffer to realize a third-order elliptic low-pass filter. In the same year, using inductor substitution and Bruton transformation methods to realize an LC ladder filter was proposed [11]. To realize a third-order voltage-mode low-pass ladder filter needs five OTAs, two of which are double-input OTAs, and three grounded capacitors. Then it was demonstrated that the two predominant methods for simulating an active LC ladder result in the same OTA-C filter circuit [12]. To Size a fourth-order shunt or series ladder arms needs seven single-input OTAs and four grounded capacitors. Recently, in order to minimize the feed-through effects or unexpected signal paths due to the finite parasitic input capacitance of the OTA, a circuit was developed which employed 3n+3 OTAs, and only one of which is double-input OTA, and n grounded capacitors to realize a general voltage-mode nth-order transfer function [13].
TABLE 1Comparison of recently reported high-Order OTA-C filtersAdvantagesEmployment ofThe lesast numberEmpolyment ofgroundedThe least numberMethodsof OTAssingle-input OTAscapacitorsof capacitorsTan andNo (23 for 8th-YesYesNo (10 for 8th-Schaumann inorder band-pass)order band-pass)1989 [1]Ananda Mohan inNo (8 for 3rd-orderNo (e.g. 3 single-YesNo (4 for 3rd-order1991 [2]low-passinput but 4 double-low-pass)input OTAsSun and Fidler inNo (2n + 2 for nth-No (e.g. n + 2YesYes1993 [3]order transfersingle-input but nfunctions)double-inputOTAs)Hwang et al. inNo (7 for 3rd-orderNo (e.g. 3 single-YesNo (4 for 3rd-order1994 [4]low-pass)input but 4 double-low-pass)input OTAsRamirez-Angulo etYes (sometimes)NoYesYesal.No (sometimes)In 1994 [5]Tsukutani et al.No (2n + 2 for nth-YesYesYesin 1996 [6]order transferfunctions)Sun and Fidler inNo (2n for (n − 1)th-No (e.g. n + 1YesNo (n for (n − 1)th-1996 [7]order transfersingle-input but n − 1order transferfunctions)double-inputfunctions)OTAs)Monir and Al-Yes (sometimes)YesYesYesHashini in 1997No (sometimes)[8]Sun and Fidler inNo (2n + 2 for nth-No (e.g. n + 2YesYes1997 [9]order transfersingle-input but nfunctions)double-inputOTAs)Wu and El-MasryNo (7 for 5th-orderYes (sometimes)YesYes (sometimes)in 1998 [10]low-pass)No (sometimes)No (sometimes)Sun in 1998 [11]Yes (sometimes)No (e.g. 3 single-Yes (sometimes)YesNo (sometimes)input but 2 double-No (sometimes)input OTAs)Schaumann inNo (7 for 4th-orderYesYesYes (4 for 4thorder1998 [12]ladder arms)ladder arms)Barbargires in 199No (3n + 3 for nth-No (e.g. 3n + 2YesYes[13]order transfersingle-input but 1functions)double-inputOTAs)Sun and FidlerNo (2n + 2/2n + 3 forYesYesYes(CM) in 1996 [14]nth-order filters)
In the traditional voltage-mode or current-mode high-order Operational Transconductance Amplifiers and Capacitors (OTA-C) filter field, if other conditions are the same that the smaller the R (resistance) or/and the C (capacitance) are used then the operational frequency is higher for an active-RC circuit. However, to cover the effect of the parasitic capacitance, the capacitor used is much larger in magnitude than the parasitic capacitance has. On the other hand, the limited adjustable range of the transconductance of an operational transconductance amplifier (OTA) leads to the limited range of operational frequency of an OTA-C filter. In other words, the operational frequency of an OTA-C filter is limited by the magnitude of the given capacitor, which cannot be too small to mask the effect of the parasitic capacitance, and the adjustable range of the transconductance of an OTA.
So far no one has resolved the given capacitor with the parasitic capacitance problem to obtain a circuit suitable for high frequency operation. One of the main reasons is that all of the positions of parasitic capacitances are not exactly at the same positions of all of the given capacitors in a realized circuit. The number of the positions of parasitic capacitances is larger than that of the positions of the given capacitors in the circuits due to several different kinds of parasitic capacitances, namely, input and output parasitic capacitances of the OTAs, and the nodal parasitic capacitance at each node in a synthesized circuit Therefore, the replacement of the given capacitors with parasitic capacitances leads to a completely different circuit structure and output response.
However, in the new nth-order OTA-C filter structures proposed in this invention there are just n grounded capacitors and just n nodes in a realized nth-order circuit All of the parasitic capacitances are just located at all of the same positions of the n given capacitors. It leads to the possibility that to replace all the given capacitors with all the parasitic capacitances doesn't change the output response at all. Such nth-order OTA-only-without-R-and-C filter structures are constructed by utilizing this unique characteristic.
Over the last decade or so numerous voltage-mode and current-mode high-order OTA-C filter structures have been reported. Such structures have often been developed with different design criteria in mind, including reduced number of active elements, single-ended-input OTAs, grounded capacitors, and simple design methods. There are three important criteria that need to be considered when generating OTA-C filter structures. The three important criteria (“Three Criteria”) are:                filters use grounded capacitors because they have smaller chip area than the floating counterpart, and because they can absorb equivalent shunt capacitive parasitics;        filters employ only single-ended-input OTAs to overcome the feed-through effects due to finite input parasitic capacitances associated with double-input OTAs; and        filters have the least number of components (passive and active) for a given order to reduce power consumption, chip areas, and noise.        
Based upon the above three important criteria, none of the current OTA filter designs are capable of achieving the three important criteria simultaneously and without trade-offs. Therefore, there is still a need to develop new nth-order filter structures that offer more advantages than existing structures. All of the circuits proposed in this invention are the perfect cases achieving the aforementioned three important criteria simultaneously.